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Theorem bj-omssind 10059
 Description: is included in all the inductive sets (but for the moment, we cannot prove that it is included in all the inductive classes). (Contributed by BJ, 30-Nov-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-omssind Ind

Proof of Theorem bj-omssind
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfcv 2178 . . 3
2 nfv 1421 . . 3 Ind
3 bj-indeq 10053 . . . 4 Ind Ind
43biimprd 147 . . 3 Ind Ind
51, 2, 4bj-intabssel1 9929 . 2 Ind Ind
6 bj-dfom 10057 . . 3 Ind
76sseq1i 2969 . 2 Ind
85, 7syl6ibr 151 1 Ind
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1243   wcel 1393  cab 2026   wss 2917  cint 3615  com 4313  Ind wind 10050 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-v 2559  df-in 2924  df-ss 2931  df-int 3616  df-iom 4314  df-bj-ind 10051 This theorem is referenced by:  bj-om  10061  peano5set  10064
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